# Three Questions

1. Oct 12, 2009

### Unknown9

1. The problem statement, all variables and given/known data
Implicit Differentiation:Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
x2/3 + y2/3 = 4 at (-3*31/2,1)

2. Relevant equations
??? None?

3. The attempt at a solution
2/3 * x-1/3 + 2/3y-1/3*y' = 0
then after a few steps of switching the sides of the variables

y' = (-2x1/3)/ 2/3*y-1/3

The part that I'm just confused on is putting x into the variables, especially since we're not suppose to use calculators, any help?

2. Oct 12, 2009

### Dick

3*3^(1/2)=3^(3/2). Does that help you simplify the x part?

3. Oct 12, 2009

### Unknown9

I think I got it, does the slope end up being -3*31/2??? Otherwise I did it incorrectly :P

4. Oct 12, 2009

### Dick

Yes, I think it does. It always helps to show your work when asking question like this.

5. Oct 14, 2009

### Unknown9

Wait wait wait, okay, when I plug in x..... how can I plug in a negative number into that....? -3^3/2 into x^- 1/3?????

6. Oct 14, 2009

### Dick

x^(-1/3) is one over the cube root of x. There isn't any problem with taking the cube roots of negative numbers.